Wireless receiver for turbo loop multiuser detection incorporating reuse of QR component

ABSTRACT

An improved receiver design implements a method for modeling users in SIC turbo loop multiuser detection architectures that reduces the number of implementation cycles, and thereby reduces the computational overhead associated with computing the inverse of the received signal covariance matrix, by efficiently reusing components of a QR decomposition. By reusing some of the computational results from the previous turbo loop&#39;s equalizer calculation, the disclosed receiver significantly reduces the computational burden of updating the linear equalizer on each turbo loop. Depending on the embodiment, this reduction can be accomplished in at least two different ways, depending on the dimensionality and other aspects of the implementation.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/838,258, titled, “Improved Wireless Receiver For Turbo Loop MultiuserDetection Incorporating Reuse Of QR Component,” filed on Dec. 11, 2017,which is a continuation of U.S. Pat. No. 9,843,462, titled, “ImprovedWireless Receiver For Turbo Loop Multiuser Detection Incorporating ReuseOf QR Component,” filed on Apr. 8, 2016, the entire disclosure of whichis here incorporated by reference, the entire disclosure of each is hereincorporated by reference.

FIELD

The invention relates to receivers used in wireless communicationnetworks, and more particularly, to receivers that are configured forturbo loop multiuser detection in wireless telecommunication.

BACKGROUND

Multiuser detection (“MUD”) is an effective approach for detectingmultiple, simultaneous data streams transmitted by a plurality offrequency sources (generically referred to herein as “users”) on acommon frequency channel, thereby providing a significant increase inthe spectral efficiency of the communication network. Applicationsinclude, but are not limited to, cellular telephone communication ofvoice and data to and from cellular handsets, other wireless mobiledevices, and wireless base stations.

Several methods can be used to perform multiuser detection, includingminimum mean-square error (MMSE), zero forcing (ZF), maximum-likelihooddetection (MLD), and such like. MLD provides the best performance, butat the cost of very high implementation complexity. Therefore, lesscomplex but close to optimal non-linear successive interferencecancellation (SIC) based receiver architectures involving turbo loopshave recently become very attractive.

In a turbo looped architecture, so as to further reduce complexity,linear MMSE-IRC (interference rejection combining) equalization isgenerally performed on data streams in successive turbo loops. However,as the dimensions of equalization increase, due for example to anincrease in the number of users and/or the number of antennas used in aMIMO multiuser system, the computational complexity increases at a ratethat is more than linear.

Most of the computational complexity of a linear MMSE equalization isassociated with computing the inverse of the received signal'scovariance matrix. Several efficient numerical methods of obtaining thesolution of a linear system can be found in the literature, such as QRdecomposition, Gauss-Jordan elimination, Cholesky decomposition, andsuch like. Among these methods, QR decomposition followed by backwardand forward substitution has been shown to be robust in achieving a highaccuracy solution without any need to compute the covariance matrix andwithout performing an actual matrix inversion. However, even whenimplementing QR decomposition there can be significant, potentiallyimpractical computational overhead (in terms of MIPS) when implementinga turbo loop based approach, even for a moderately large MIMO multiusersystem.

It is therefore essential for meeting standard product release criteriato develop methods that reduce the computational complexity of aturbo-looped implementation, while retaining near-optimal turbo-loopperformance.

What is needed, therefore, is an improved receiver design for modelingusers in SIC turbo loop multiuser detection architectures that reducesthe computational complexity of the turbo-looped implementation whileretaining near-optimal turbo-loop performance.

SUMMARY

An improved receiver design implements a method for modeling users inSIC turbo loop multiuser detection architectures having a reducedcomputational overhead, so that the receiver design is applicable topractical, “real world” communication networks that have reasonably highdegrees of complexity. The disclosed method reduces the number ofimplementation cycles, and thereby reduces the computational overheadassociated with computing the inverse of the received signal covariancematrix, by efficiently reusing components of a QR decomposition.

For near optimality, it is necessary for a turbo SIC receiver to updatethe linear equalizer on each turbo loop. This can add significantcomputational overhead, because it requires a matrix inversion. Byreusing some of the computational results from the previous turbo loop'sequalizer calculation, the disclosed receiver significantly reduces thiscomputational burden. Depending on the embodiment, this reduction can beaccomplished in at least two different ways, depending on thedimensionality and other aspects of the implementation.

A first general aspect of the disclosed method for efficientlyestimating a plurality of unknown values included in a signaltransmitted over a subcarrier of a transmission by a signal sourceincludes receiving the signal from the signal source, and in a firstturbo loop:

-   -   a) estimating an interference plus noise covariance matrix        according to a residual signal either received during a period        when the signal source is not transmitting, or obtained by        removing known values of the signal from a received training        vector;    -   b) determining an equalizer function;    -   c) obtaining estimates of the unknown values by applying the        equalizer function to the received signal;    -   d) deriving a residual signal by subtracting the value estimates        from the received signal; and    -   e) determining a residual amplitude matrix representing value        amplitudes that remain after the subtraction of step d).

The method further includes repeating steps b), c), and d) in at leastone turbo loop following the first turbo loop until estimates of theplurality of unknown values are obtained, each loop being applied to theresidual signal vector and residual amplitude matrix obtained in thepreceding loop.

According to the method, determining the equalizer function in step b)of the first turbo loop includes performing a QR decomposition, anddetermining the equalizer function in step b) of turbo loops after thefirst turbo loop includes performing calculations that incorporate atleast a partial result of the QR decomposition.

A first general aspect of the disclosed apparatus for efficientlyestimating a plurality of unknown values included in a signaltransmitted over a subcarrier of a transmission by a signal sourceincludes a receiver unit and a signal processing unit. The receiver unitis configured to receive the signal from the signal source. The signalprocessing unit is configured in a first turbo loop to:

-   -   a) estimate an interference plus noise covariance matrix        according to a residual signal either received during a period        when the signal source is not transmitting, or obtained by        removing known values of the signal from a received training        vector;    -   b) determine an equalizer function;    -   c) obtain estimates of the unknown values by applying the        equalizer function to the received signal;    -   d) derive a residual signal by subtracting the value estimates        from the received signal; and    -   e) determine a residual amplitude matrix representing value        amplitudes that remain after the subtraction of step d).

The signal processing unit is further configured to repeat steps b), c),and d) in at least one turbo loop following the first turbo loop untilestimates of the plurality of unknown values are obtained, each loopbeing applied to the residual signal vector and residual amplitudematrix obtained in the preceding loop,

According to this first aspect, determining the equalizer function instep b) of the first turbo loop includes performing a QR decomposition,and determining the equalizer function in step b) of turbo loops afterthe first turbo loop includes performing calculations that incorporateat least a partial result of the QR decomposition.

A second general aspect of the disclosed apparatus includes anon-transitory computer readable medium storing a computer program,executable by a machine, for efficiently estimating a plurality ofunknown values included in a signal transmitted over a subcarrier of atransmission by a signal source, the computer program comprisingexecutable instructions for:

-   -   receiving the signal from the signal source;    -   in a first turbo loop:        -   a) estimating an interference plus noise covariance matrix            according to a residual signal either received during a            period when the signal source is not transmitting, or            obtained by removing known values of the signal from a            received training vector;        -   b) determining an equalizer function;        -   c) obtaining estimates of the unknown values by applying the            equalizer function to the received signal;        -   d) deriving a residual signal by subtracting the value            estimates from the received signal; and        -   e) determining a residual amplitude matrix representing            value amplitudes that remain after the subtraction of step            d);    -   and:        -   repeating steps b), c), and d) in at least one turbo loop            following the first turbo loop until estimates of the            plurality of unknown values are obtained, each loop being            applied to the residual signal vector and residual amplitude            matrix obtained in the preceding loop.

According to this second aspect, determining the equalizer function instep b) of the first turbo loop includes performing a QR decomposition,and determining the equalizer function in step b) of turbo loops afterthe first turbo loop includes performing calculations that incorporateat least a partial result of the QR decomposition.

The features and advantages described herein are not all-inclusive and,in particular, many additional features and advantages will be apparentto one of ordinary skill in the art in view of the drawings,specification, and claims. Moreover, it should be noted that thelanguage used in the specification has been principally selected forreadability and instructional purposes, and not to limit the scope ofthe inventive subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings provide visual representations which will beused to more fully describe the representative embodiments disclosedhere and can be used by those skilled in the art to better understandthem and their inherent advantages. In these drawings, like referencenumerals identify corresponding elements, and:

FIG. 1 is a flow diagram illustrating an embodiment of the methoddisclosed herein;

FIG. 2 is a flow diagram illustrating a method for calculating W in anembodiment of the method disclosed herein;

FIG. 3 is a flow diagram illustrating an alternate method forcalculating W in an embodiment of the method disclosed herein; and

FIG. 4 is a block diagram illustrating an embodiment of the disclosedsystem.

DETAILED DESCRIPTION

An improved receiver design implements a method for modeling users inSIC turbo loop multiuser detection architectures having a reducedcomputational overhead. For near optimality, it is necessary for a turboSIC receiver to update the linear equalizer on each turbo loop. This canadd significant computational overhead, because it requires a matrixinversion. By reusing some of the computations from the previous turboloop's equalizer calculation, the disclosed receiver significantlyreduces this computational burden.

According to the disclosed method, during the first application of thelinear equalizer (e.g. MMSE-IRC), before the forward error correctiondecoder, a matrix QR decomposition is computed to evaluate the equalizeroutput. From samples of the received signal acquired at a plurality oftimes, frequencies, and/or locations, the equalizer computes a singleestimate of the transmitted information or “symbol.” Note that the term“symbol” is used generically herein to refer to received information,and is not limited only to information derived from a symbolconstellation, as would be the case for SC-FDMA. For simplicity ofexplanation, OFDM (Orthogonal Frequency Division Multiplexing) is usedherein as an illustrative example. However, one of skill in the art willappreciate that the scope of the disclosed method is not limited toOFDM.

With reference to FIGS. 1-4, given a vector of transmitted symbols, s,received from one or more signal sources, the signal vector r received100 over a single subcarrier in a multiple antenna receiver 402 is givenby:r=Hs+i+n.  (1)where H is the mixture matrix (spatial mixture in this case), i is theinterference from other environmental sources, and n is thermal noise inthe receiver. The interference plus noise (i+n) is assumed to have acovariance matrix C given by:E[(i+n)(i+n)^(H)]=C  (2)

The equalizer, W, provides an estimate ŝ of the transmitted symbol, s,according 108 to:ŝ=W ^(H) r  (3)The choice of W can be based on many criteria but is typically computedby inverting a matrix comprising a plurality of the transmissionparameters. As an example, the MMSE-IRC linear equalizer can be givenby:W=(HH ^(H) +C+λ ² I)⁻¹ H  (4)This formula for determining the equalizer is adopted herein because itis optimal, in some sense, and because many suboptimal options areapproximations of this solution. In equation 4, I is an identity matrix,and λ is a constant that is used to “regularize” the inverse in case itis singular, or there is a large variance in the estimate of C.

Due to the computational complexity, as described above, in embodimentsof the present method the matrix inverse indicated in equation 4 is notdirectly calculated. Instead, in embodiments, the disclosed receiversolves the system of equations:(HH ^(H) +C+λ ² I)W=H  (5)The matrix (HH^(H)+C+λ²I) is referred to as the “covariance matrix.”Because the covariance is positive definite, it can be decomposed intosquare root matrices:(HH ^(H) +C+λ ² I)=R ^(H) R  (6)

In practice the receiver does not know C ahead of time and must estimateit 102. This is typically done by estimating the interference when thesignal of interest, s, is not present, or during a training period whenthe influence of the desired signal s can be removed (e.g. during a DRMSin LTE). The signal when s is not present (or has been removed) isreferred to herein as the background signal, {tilde over (r)}.Accordingly, in embodiments, C is estimated by averaging the outerproduct of N observations of {tilde over (r)}, where the estimate Ĉ isgiven by

$\begin{matrix}{\hat{C} = {\frac{1}{N}{\sum{\overset{\sim}{r}\;{\overset{\sim}{r}}^{H}}}}} & (7)\end{matrix}$

Based on the above, an important enabling concept for the disclosedmethod is the fact that:

$\begin{matrix}{\left( {{HH}^{H} + C + {\lambda^{2}I}} \right) = {\begin{bmatrix}H & {\frac{1}{\sqrt{N}}\overset{\sim}{r}} & {\lambda\; I}\end{bmatrix}\begin{bmatrix}H^{H} \\{\frac{1}{\sqrt{N}}{\overset{\sim}{r}}^{H}} \\{\lambda\; I}\end{bmatrix}}} & (9)\end{matrix}$Accordingly, the standard QR decomposition can be taken on the matrix:

$\begin{matrix}{\begin{bmatrix}H^{H} \\{\frac{1}{\sqrt{N}}{\overset{\sim}{r}}^{H}} \\{\lambda\; I}\end{bmatrix} = {QR}} & (10)\end{matrix}$where Q is unitary and R is upper triangular. Because Q is a unitarymatrix, the R matrix in equation 10 is a matrix square root of thecovariance matrix as desired, i.e.:(HH ^(H) +C+λ ² I)=R ^(H) R  (11)Based on this relationship, the equalizer equation 5 can be re-writtenas:R ^(H) RW=H  (12)and solved 106 for W using forward and backward substitution on theupper triangular matrix R.

After the first turbo loop, a significant amount of energy from eachsymbol is subtracted from the received signal vector r, to obtain 110 aresidual signal r₂, where the subscript “2” indicates that this is thesignal vector to which the second turbo loop will be applied. Note thatr can similarly be designated as r₁ because it is the signal vector towhich the first turbo loop is applied. This has the effect of changingthe optimal equalizer by adjusting scale (energy) of the columns of thesymbol mixing matrix H. The new signal vector r₂ to which the secondturbo loop is applied is then given by:r ₂ =HA ₂ s+i+n  (13)where A₂ is a diagonal matrix representing the amplitude remaining foreach symbol after SIC on turbo loop 2, and in general A_(i) representsthe amplitude remaining for each symbol after SIC on turbo loop i. Ofcourse, A₁ does not explicitly appear in equation 1 because A₁ is theidentity matrix. Note that equation 13 can be written as:r ₂ =r−H

  (14)where

is the vector of estimates that were subtracted from r₁ in turbo loopone. This has the effect of changing the MMSE-IRC equalizer equation to:W=(HA ₂ ² H ^(H) +C+λI)⁻¹ H  (15)Also note that Wr₂ is the revised estimate for each symbol, and that thefinal equalized output on turbo loop 2 is given by:

=

+diag(H ^(H) W)⁻¹ W ^(H) r ₂  (16)where diag(H^(H)W) is the diagonal matrix taken from H^(H)W, which is ascaling factor necessary to make the estimate unbiased.

In general, to solve the equalization problem on turbo loop n, it isnecessary to find the QR decomposition of (HA_(n) ²H^(H)+C+λ²I), and tosolve the resulting system of equations. An important enabling conceptof the disclosed method is the approach of using a partial result of theQR decomposition from the first turbo loop to significantly reduce thecomputational overhead in subsequent turbo loops. In particular, thematrix C+λ²I does not change between turbo loops, which means that itsQR decomposition can be computed once, during the first turbo loop, andthen reused during subsequent turbo loops so as to reduce thecomputational overhead in calculating the total QR decomposition.

For example, let:

$\begin{matrix}{\begin{bmatrix}{\frac{1}{\sqrt{N}}{\overset{\sim}{r}}^{H}} \\{\lambda\; I}\end{bmatrix} = {Q_{r}\mspace{11mu} R_{r}}} & (17)\end{matrix}$where Q_(r), is a unitary matrix and R_(r) is upper triangular. Then itcan be seen that:

$\begin{matrix}{\begin{bmatrix}{A_{n}H^{H}} \\{\frac{1}{\sqrt{N}}{\overset{\sim}{r}}^{H}} \\{\lambda\; I}\end{bmatrix} = {\begin{bmatrix}1 & 0 \\0 & Q_{r}\end{bmatrix}\begin{bmatrix}{A_{n}H^{H}} \\R_{r}\end{bmatrix}}} & (18)\end{matrix}$Note that because R_(r), is already upper triangular, it issignificantly easier to do a QR decomposition on

$\quad\begin{bmatrix}{A_{n}H^{H}} \\R_{r}\end{bmatrix}$than on

$\quad{\begin{bmatrix}{A_{n}H^{H}} \\{\frac{1}{\sqrt{N}}{\overset{\sim}{r}}^{H}} \\{\lambda\; I}\end{bmatrix},}$and that the final upper triangular matrix R will still be correct.Therefore, in embodiments the disclosed receiver is configured tocalculate R_(r) on the first turbo loop 104, and then to store it forreuse in all successive turbo loops.

In other embodiments, the following alternative, but equivalent,equation is used to determine the equalizer in turbo loop n:W ^(H) =A _(n) ⁻²[A _(n) ⁻² +H ^(H) C ⁻¹ H]⁻¹ H ^(H) C ⁻¹  (19)In these embodiments, the equalizer W is implemented differently. On thefirst turbo loop, the receiver solves a system of two linear equations,and then the solution is reused on all subsequent turbo loops.

In various embodiments, the receiver begins by calculating the QRdecomposition of equation 17:

$\begin{bmatrix}{\frac{1}{\sqrt{N}}{\overset{\sim}{r}}^{H}} \\{\lambda\; I}\end{bmatrix} = {Q_{r}\mspace{11mu}{R_{r}.}}$

In this case R_(r) is a matrix square root of C, with someregularization for numerical and estimation stability. The receiver thensolves the system of equations 300:R _(r) ^(H) m=H  (20)and derives:m=C ^(−1/2) H  (21)Next, the receiver solves 304 the equation:R _(r) q=m  (22)for q to obtain:q=C ⁻¹ H  (23)These quantities, determined in the first turbo loop, can then be storedand used in every subsequent turbo loop, which can be clearly seen fromequation 19.

Finally, the receiver solves the equation(A _(n) ⁻² +H ^(H) C ⁻¹ H)W ^(H) =H ^(H) C ⁻¹  (24)for W^(H). In embodiments, the receiver solves equation 24 by finding302 the QR decomposition of:

$\begin{matrix}{\begin{bmatrix}m \\A_{n}^{- 1}\end{bmatrix} = {Q_{n}\mspace{11mu} R_{n}}} & (25)\end{matrix}$and then solving 306 the equation:R _(n) ^(H) R _(n) W ^(H) =q ^(H) =H ^(H) C ⁻¹  (26)

Accordingly, instead of computing a full QR decomposition on

$\quad\begin{bmatrix}{C^{{- 1}/2}H^{H}A_{n}} \\I\end{bmatrix}$in each turbo loop, as some previous approaches may have done, thecomputational overhead is significantly decreased in these embodimentsby reformulating and solving the system in a different way that exploitsresults obtained in previous turbo loop computations, as well as thefact that the matrix A is diagonal.

With reference to FIG. 4, the system disclosed herein 400 includes asignal receiving unit 402 in communication with at least one antenna 404and configured to receive a transmission including data streams from aplurality of signal sources, and a signal processing unit 406 thatperforms computations indicated in FIGS. 1-3.

The controller 406 is an instruction execution machine, apparatus, ordevice and may comprise one or more of a microprocessor, a digitalsignal processor, a graphics processing unit, an application specificintegrated circuit (ASIC), a field programmable gate array (FPGA), andthe like. The controller 406 may be configured to execute programinstructions stored in a memory and/or data storage (both not shown).The memory may include read only memory (ROM) and random access memory(RAM). The data storage may include a flash memory data storage devicefor reading from and writing to flash memory, a hard disk drive forreading from and writing to a hard disk, a magnetic disk drive forreading from or writing to a removable magnetic disk, and/or an opticaldisk drive for reading from or writing to a removable optical disk suchas a CD ROM, DVD or other optical media. The drives and their associatedcomputer-readable media provide nonvolatile storage of computer readableinstructions, data structures, program modules and other data.

It is noted that the methods described herein can be embodied inexecutable instructions stored in a computer readable medium for use byor in connection with an instruction execution machine, apparatus, ordevice, such as a computer-based or processor-containing machine,apparatus, or device. It will be appreciated by those skilled in the artthat for some embodiments, other types of computer readable media may beused which can store data that is accessible by a computer, such asmagnetic cassettes, flash memory cards, digital video disks, Bernoullicartridges, RAM, ROM, and the like may also be used in the exemplaryoperating environment. As used here, a “computer-readable medium” caninclude one or more of any suitable media for storing the executableinstructions of a computer program in one or more of an electronic,magnetic, optical, and electromagnetic format, such that the instructionexecution machine, system, apparatus, or device can read (or fetch) theinstructions from the computer readable medium and execute theinstructions for carrying out the described methods. A non-exhaustivelist of conventional exemplary computer readable medium includes: aportable computer diskette; a RAM; a ROM; an erasable programmable readonly memory (EPROM or flash memory); optical storage devices, includinga portable compact disc (CD), a portable digital video disc (DVD), ahigh definition DVD (HD-DVD™), a BLU-RAY disc; and the like.

The controller 306 and receiver 402 preferably detect and analyzetransmissions from a base station (“BS”) that operates in a networkedenvironment using logical connections to one or more remote nodes (notshown). The remote node may be another BS, a UE, a computer, a server, arouter, a peer device or other common network node. The base station mayinterface with a wireless network and/or a wired network. For example,wireless communications networks can include, but are not limited to,Code Division Multiple Access (CDMA), Time Division Multiple Access(TDMA), Frequency Division Multiple Access (FDMA), Orthogonal FrequencyDivision Multiple Access (OFDMA), and Single-Carrier Frequency DivisionMultiple Access (SC-FDMA). A CDMA network may implement a radiotechnology such as Universal Terrestrial Radio Access (UTRA),Telecommunications Industry Association's (TIA's) CDMA2000®, and thelike. The UTRA technology includes Wideband CDMA (WCDMA), and othervariants of CDMA. The CDMA2000® technology includes the IS-2000, IS-95,and IS-856 standards from The Electronics Industry Alliance (EIA), andTIA. A TDMA network may implement a radio technology such as GlobalSystem for Mobile Communications (GSM). An OFDMA network may implement aradio technology such as Evolved UTRA (E-UTRA), Ultra Mobile Broadband(UMB), IEEE 802.11 (Wi-Fi), IEEE 802.16 (WiMAX), IEEE 802.20,Flash-OFDMA, and the like. The UTRA and E-UTRA technologies are part ofUniversal Mobile Telecommunication System (UMTS). 3GPP Long TermEvolution (LTE) and LTE-Advance (LTE-A) are newer releases of the UMTSthat use E-UTRA. UTRA, E-UTRA, UMTS, LTE, LTE-A, and GAM are describedin documents from an organization called the “3rd Generation PartnershipProject” (3GPP). CDMA2000® and UMB are described in documents from anorganization called the “3rd Generation Partnership Project 2” (3GPP2).The techniques described herein may be used for the wireless networksand radio access technologies mentioned above, as well as other wirelessnetworks and radio access technologies. Other examples of wirelessnetworks include, for example, a BLUETOOTH network, a wireless personalarea network, and a wireless 802.11 local area network (LAN).

Examples of wired networks include, for example, a LAN, a fiber opticnetwork, a wired personal area network, a telephony network, and/or awide area network (WAN). Such networking environments are commonplace inintranets, the Internet, offices, enterprise-wide computer networks andthe like. In some embodiments, a communication interface may includelogic configured to support direct memory access (DMA) transfers betweenmemory and other devices.

It should be understood that the arrangement illustrated in FIG. 4 isbut one possible implementation, and that other arrangements arepossible. It should also be understood that the various systemcomponents (and means) defined by the claims, described above, andillustrated in the various block diagrams represent logical componentsthat are configured to perform the functionality described herein. Forexample, one or more of these system components (and means) can berealized, in whole or in part, by at least some of the componentsillustrated in the arrangement of hardware device 400. In addition,while at least one of these components are implemented at leastpartially as an electronic hardware component, and therefore constitutesa machine, the other components may be implemented in software,hardware, or a combination of software and hardware. More particularly,at least one component defined by the claims is implemented at leastpartially as an electronic hardware component, such as an instructionexecution machine (e.g., a processor-based or processor-containingmachine) and/or as specialized circuits or circuitry (e.g., discretelogic gates interconnected to perform a specialized function), such asthose illustrated in FIG. 4. Other components may be implemented insoftware, hardware, or a combination of software and hardware. Moreover,some or all of these other components may be combined, some may beomitted altogether, and additional components can be added while stillachieving the functionality described herein. Thus, the subject matterdescribed herein can be embodied in many different variations, and allsuch variations are contemplated to be within the scope of what isclaimed.

In the description above, the subject matter is described with referenceto acts and symbolic representations of operations that are performed byone or more devices, unless indicated otherwise. As such, it will beunderstood that such acts and operations, which are at times referred toas being computer-executed, include the manipulation by the processingunit of data in a structured form. This manipulation transforms the dataor maintains it at locations in the memory system of the computer, whichreconfigures or otherwise alters the operation of the device in a mannerwell understood by those skilled in the art. The data structures wheredata is maintained are physical locations of the memory that haveparticular properties defined by the format of the data. However, whilethe subject matter is being described in the foregoing context, it isnot meant to be limiting as those of skill in the art will appreciatethat various of the acts and operation described hereinafter may also beimplemented in hardware.

To facilitate an understanding of the subject matter disclosed, manyaspects are described in terms of sequences of actions. At least one ofthese aspects defined by the claims is performed by an electronichardware component. For example, it will be recognized that the variousactions can be performed by specialized circuits or circuitry, byprogram instructions being executed by one or more processors, or by acombination of both. The description herein of any sequence of actionsis not intended to imply that the specific order described forperforming that sequence must be followed. All methods described hereincan be performed in any suitable order unless otherwise indicated hereinor otherwise clearly contradicted by context.

The use of the terms “a” and “an” and “the” and similar referents in thecontext of describing the subject matter (particularly in the context ofthe following claims) are to be construed to cover both the singular andthe plural, unless otherwise indicated herein or clearly contradicted bycontext. Recitation of ranges of values herein are merely intended toserve as a shorthand method of referring individually to each separatevalue falling within the range, unless otherwise indicated herein, andeach separate value is incorporated into the specification as if it wereindividually recited herein. Furthermore, the foregoing description isfor the purpose of illustration only, and not for the purpose oflimitation, as the scope of protection sought is defined by the claimsas set forth hereinafter together with any equivalents thereof entitledto. The use of any and all examples, or exemplary language (e.g., “suchas”) provided herein, is intended merely to better illustrate thesubject matter and does not pose a limitation on the scope of thesubject matter unless otherwise claimed. The use of the term “based on”and other like phrases indicating a condition for bringing about aresult, both in the claims and in the written description, is notintended to foreclose any other conditions that bring about that result.No language in the specification should be construed as indicating anynon-claimed element as essential to the practice of the invention asclaimed.

Preferred embodiments are described herein, including the best modeknown to the inventor for carrying out the claimed subject matter. Oneof ordinary skill in the art should appreciate after learning theteachings related to the claimed subject matter contained in theforegoing description that variations of those preferred embodiments maybecome apparent to those of ordinary skill in the art upon reading theforegoing description. The inventor intends that the claimed subjectmatter may be practiced otherwise than as specifically described herein.Accordingly, this claimed subject matter includes all modifications andequivalents of the subject matter recited in the claims appended heretoas permitted by applicable law. Moreover, any combination of theabove-described elements in all possible variations thereof isencompassed unless otherwise indicated herein or otherwise clearlycontradicted by context.

We claim:
 1. A method for efficiently estimating a plurality of unknownvalues included in a signal transmitted over a subcarrier of atransmission by a signal source, the method comprising: receiving thesignal from the signal source; and applying a turbo loop to the receivedsignal until estimates of the plurality of unknown values aredetermined, the turbo loop comprising: obtaining estimates of theunknown values by applying an equalizer determined based on a QRdecomposition, wherein a QR decomposition on a subsequent turbo loop isbased on a QR decomposition of a previous loop; and applying theequalized signal to a residual signal vector and a residual amplitudematrix, the residual signal vector determined by subtracting theestimates of the unknown values from the received signal and theresidual amplitude matrix representing value amplitudes that remainafter the estimates of the unknown values are subtracted.
 2. The methodof claim 1, wherein: receiving the signal includes obtaining a receivedsignal vector r that includes N observations of the signal, r beinggiven by r=H s+i+n, where s is a vector representing the plurality ofunknown values transmitted by the signal source, H is a mixture matrix,i represents interference included in the received signal, and nrepresents thermal receiver noise included in the received signal; theQR decomposition of a first turbo loop includes obtaining an uppertriangular matrix R_(r) by solving an equation ${\begin{bmatrix}{\frac{1}{\sqrt{N}}{\overset{\sim}{r}}^{H}} \\{\lambda\; I}\end{bmatrix} = {{Qr}\mspace{11mu}{Rr}}},$ where λ is a constant, I isan identity matrix, {tilde over (r)} is a background signal when s isnot present or has been removed, and Q_(r) is a unitary matrix; andincorporating at least a partial result of the QR decomposition of turboloops after the first turbo loop includes performing calculations thatincorporate at least part of the matrix R_(r).
 3. The method of claim 2,wherein applying an equalizer determined based on a QR decompositionincludes applying an equalizer function W that is a solution to anequation RH R W=H, where: R is an upper triangular matrix solution to anequation ${\begin{bmatrix}{AH}^{H} \\R_{r}\end{bmatrix} = {QR}};$ Q is a unitary matrix; and A is a diagonalmatrix representing value amplitudes that remain after the subtractionof the value estimates from the received signal.
 4. The method of claim2, wherein applying an equalizer determined based on a QR decompositionincludes applying an equalizer function W that is a solution to anequation R_(n) ^(H) R_(n) WH=qH, where: q is a solution to an equationR_(r) q=m; m is a solution to an equation R_(r) ^(H) m=H; R_(n) is anupper triangular matrix solution to an equation ${\begin{bmatrix}m \\A^{- 1}\end{bmatrix} = {Q_{n}\mspace{11mu} R_{n}}};$ Q_(n) is a unitary matrix;A is a diagonal matrix representing value amplitudes that remain afterthe subtraction of the value estimates from the received signal andperforming calculations that incorporate at least part of the matrixR_(r) in turbo loop as after the first turbo loop includes sharing atleast one of R_(r), m, and q between successive turbo loops.
 5. Themethod of claim 2, wherein obtaining the estimates of unknown valuesincludes obtaining a vector ŝ of value estimates by applying anequalizer function W to r according to the equation ŝ=WHr.
 6. The methodof claim 5, wherein determining the residual signal includes deriving aresidual signal vector rr by subtracting the value estimates ŝ from thereceived signal vector r according to the equation rr=r−Hŝ.
 7. Themethod of claim 5, wherein the residual amplitude matrix A is determinedaccording to an equation s−ŝ=A s, where A is a diagonal matrixrepresenting value amplitudes that remaining after subtracting the valueestimates.
 8. The method of claim 1, wherein at least one of the turboloops following the first turbo loop further includes repeating applyingthe residual amplitude matrix.
 9. The method of claim 1, wherein atleast one of the turbo loops includes improving the estimates of thevalues by decoding at least one error correction.
 10. The method ofclaim 1, wherein the unknown values transmitted by the signal source aretransmitted symbols.
 11. The method of claim 10, further comprisingpresenting the estimated symbols to a user.
 12. The method of claim 1,wherein the transmission is a transmission between nodes in a wirelesscommunication network.
 13. The method of claim 1, wherein thetransmission is a transmission between a fixed base station and a mobilehandset in a wireless cellular telecommunications network.
 14. Themethod of claim 13, wherein the transmission is encoded according to aprotocol that conforms to one of Orthogonal Frequency DivisionMultiplexing (OFDM) and Single-Carrier Frequency Division MultipleAccess (SC-FDMA).
 15. The method of claim 13, wherein the transmissionadheres to the Long Term Evolution (LTE) protocol.
 16. A system forefficiently estimating a plurality of unknown values included in asignal transmitted over a subcarrier of a transmission by a signalsource, the system comprising: a receiver unit configured to receive thesignal from the signal source; and a signal processing unit configuredto: apply a turbo loop to the received signal until estimates of theplurality of unknown values are determined, the turbo loop comprising:obtain estimates of the unknown values by applying an equalizerdetermined based on a QR decomposition, wherein a QR decomposition on asubsequent turbo loop is based on a QR decomposition of a previous loop;and apply the equalized signal to a residual signal vector and aresidual amplitude matrix, the residual signal vector determined bysubtracting the estimates of the unknown values from the received signaland the residual amplitude matrix representing value amplitudes thatremain after the estimates of the unknown values are subtracted.
 17. Thesystem of claim 16, wherein: receiving the signal includes obtaining areceived signal vector r that includes N observations of the signal, rbeing given by r=H s+i+n, where s is a vector representing the pluralityof unknown values transmitted by the signal source, H is a mixturematrix, i represents interference included in the received signal, and nrepresents thermal receiver noise included in the received signal; theQR decomposition of the first turbo loop includes obtaining an uppertriangular matrix Rr by solving the equation ${\begin{bmatrix}{\frac{1}{\sqrt{N}}{\overset{\sim}{r}}^{H}} \\{\lambda\; I}\end{bmatrix} = {Q_{r}\mspace{11mu} R_{r}}},$ where λ is a constant, Iis the unity matrix, {tilde over (r)} is a background signal when s isnot present or has been removed, and Qr is a unitary matrix; andincorporating at least a partial result of the QR decomposition in stepb) of turbo loops after the first turbo loop includes performingcalculations that incorporate at least part of the matrix Rr.
 18. Thesystem of claim 17, wherein an equalizer determined based on a QRdecomposition includes an equalizer function W that is a solution of theequation RH R W=H, where: R is an upper triangular matrix solution to anequation ${\begin{bmatrix}{AH}^{H} \\R_{r}\end{bmatrix} = {QR}};$ Q is a unitary matrix; and A is a diagonalmatrix representing value amplitudes that remain after the subtractionof the value estimates from the received signal.
 19. The system of claim17, wherein an equalizer determined based on a QR decomposition includesan equalizer function W that is the solution of the equation R_(n) ^(H)R_(n) WH=qH, where: q is an solution to an equation R_(r) q=m; m is ansolution to an equation R_(r) ^(H) m=H; R_(n) is an upper triangularmatrix solution to an equation ${\begin{bmatrix}m \\A^{- 1}\end{bmatrix} = {Q_{n}\mspace{11mu} R_{n}}};$ Q_(n) is a unitary matrix;A is a diagonal matrix representing value amplitudes that remain afterthe subtraction of the value estimates from the received signal andperforming calculations that incorporate at least part of the matrixR_(r) in turbo loop as after the first turbo loop includes sharing atleast one of R_(r), m, and q between successive turbo loops.
 20. Thesystem of claim 17, wherein obtaining the estimates of unknown valuesincludes obtaining a vector ŝ of value estimates by applying anequalizer function W to r according to the equation ŝ=WHr.
 21. Thesystem of claim 20, wherein determining the residual signal includesderiving a residual signal vector rr by subtracting the value estimatesŝ from the received signal vector r according to the equation rr=r−Hŝ.22. The system of claim 20, wherein the residual amplitude matrix A isdetermined according to an equation s−ŝ=A s, where A is a diagonalmatrix representing value amplitudes that remaining after subtractingthe value estimates.
 23. The system of claim 16, wherein at least one ofthe turbo loops following the first turbo loop further includesrepeating applying the residual amplitude matrix.
 24. The method ofclaim 16, wherein at least one of the turbo loops includes improving theestimates of the values by decoding at least one error correction. 25.The system of claim 16, wherein the unknown values transmitted by thesignal source are transmitted symbols.
 26. The system of claim 25,further comprising presenting the estimated symbols to a user.
 27. Thesystem of claim 16, wherein the transmission is a transmission betweennodes in a wireless communication network.
 28. The system of claim 16,wherein the transmission is a transmission between a fixed base stationand a mobile handset in a wireless cellular telecommunications network.29. The system of claim 16, wherein the transmission is encodedaccording to a protocol that conforms to one of Orthogonal FrequencyDivision Multiplexing (OFDM) and Single-Carrier Frequency DivisionMultiple Access (SC-FDMA).
 30. The system of claim 16, wherein thetransmission adheres to the Long Term Evolution (LTE) protocol.
 31. Anon-transitory computer readable medium storing a computer program,executable by a machine, for efficiently estimating a plurality ofunknown values included in a signal transmitted over a subcarrier of atransmission by a signal source, the computer program comprisingexecutable instructions for: receiving the signal from the signalsource; and applying a turbo loop to the received signal until estimatesof the plurality of unknown values are determined, the turbo loopcomprising: obtaining estimates of the unknown values by applying anequalizer determined based on a QR decomposition, wherein a QRdecomposition on a subsequent turbo loop is based on a QR decompositionof a previous loop; and applying the equalized signal to a residualsignal vector and a residual amplitude matrix, the residual signalvector determined by subtracting the estimates of the unknown valuesfrom the received signal and the residual amplitude matrix representingvalue amplitudes that remain after the estimates of the unknown valuesare subtracted.